In the literature, there are many 1 degree of freedom planar mechanisms, the input link of which is translating, whereas the output link is rotating. For example, in FIG. 1, the slider crank mechanism, which is a one degree of freedom, planar mechanism, is shown with the input and output parameters being denoted by si and θ0. In this mechanism, it is possible to generate, approximately, any desired torque T(θ0); and any input-output relation, given by equation (E1), by properly designing the kinematic dimensions, the free length of the spring used, and the spring constant k. Although the input-output relation given by equation (E1) and the desired torque, T(θo), can be produced only approximately in the slider crank mechanism; it is possible to generate, as much as the physical constraints allow, any desired input-output relation and any desired torque without making any approximations (i.e., exactly in the desired manner) by using mechanisms that include a cam pair and/or a cylinder in slot joint.
The slider crank mechanism shown in FIG. 1 is connected to the ground by 1 prismatic joint and 1 revolute joint. The reaction forces, reaction moments and frictional forces that occur at these 2 joints constitute the shaking forces and moments exerted on the ground. The aforementioned shaking forces and moments will depend upon the T(θ0) torque that is generated, the inertia forces and moments, due to D'Alembert's principle, that act on the moving links; and the weights of the links. In general, in this type of an application, the shaking forces and moments will, to a large extent, be due to the T(θ0) torque and the inertia forces and moments; and the contribution of the weights of the links to the shaking forces and moments will be relatively smaller.
As is well known, the shaking forces and moments cause undesirable noise and vibrations at the bearings that connect the mechanism to the ground. Due to these reasons, the mechanism works in a disturbingly noisy manner and the bearings wear out quickly. Although the measures taken to prevent the noise and the vibrations cannot provide a fully satisfactory solution, they increase the cost of the system. Furthermore, due to the friction at the 2 joints that connect the mechanism to the ground, extra energy, which adversely affects the energy consumption of the mechanism, is consumed.